Pocket formation and the flame surface density equation

摘要

The occurrence and properties of singularities in the equation for the surface density function sigma (triple-bond)(vert- bar)(del)Phi(vert-bar) are analyzed analytically and numerically using data from two dimensional direct numerical simulation (DNS) of pocket formation in a premixed methane-air flame. The sink and source terms in surface density function (SDF) are evaluated in the neighborhood of a critical point using DNS data during pocket formation, and an analytic representation of a scalar in the vicinity of the critical point which allows for the computation of all kinematic properties. The analytic and computational results show that the normal restoration and dissipation terms in the sdf become singular at the critical point when the pocket emerges. Furthermore, the analytic results show that the singularities exactly cancel, and therefore, the main conclusion is that it is unnecessary to model the singular behavior of these terms at critical points. However, closure of their sum is recommended.